In two volumes, this comprehensive treatment covers all that is needed to understand and appreciate this beautiful branch of mathematics.

An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

The Space that Separates: A Realist Theory of Art radically challenges our assumptions about what art is, what art does, who is doing it, and why it matters. Rejecting the modernist and market-driven misconception that art is only what artists do, Wilson instead presents a realist case for living artfully. Art is defined as the skilled practice of giving shareable form to our experiences of being-in-relation with the real; that is to say, the causally generative domain of the world that extends beyond our direct observation, comprising relations, structures, mechanisms, possibilities, powers, processes, systems, forces, values, ways of being. In communicating such aesthetic experience we behold life’s betweenness – "the space that separates", so coming to know ourselves as connected. Providing the first dedicated and comprehensive account of art and aesthetics from a critical realist perspective – Aesthetic Critical Realism (ACR), Wilson argues for a profound paradigm shift in how we understand and care for culture in terms of our system(s) of value recognition. Fortunately, we have just the right tool to help us achieve this transformation – and it’s called art. Offering novel explanatory accounts of art, aesthetic experience, value, play, culture, creativity, artistic truth and beauty, this book will appeal to a wide audience of students and scholars of art, aesthetics, human development, philosophy and critical realism, as well as cultural practitioners and policy-makers.

This is volume 1 of a 2 volume set.

This ambitious book investigates a major yet underexplored nexus of themes in Roman cultural history: the evolving tropes of enclosure, retreat and compressed space within an expanding, potentially borderless empire. In Roman writers' exploration of real and symbolic enclosures - caves, corners, villas, bathhouses, the 'prison' of the human body itself - we see the aesthetic, philosophical and political intersecting in fascinating ways, as the machine of empire is recast in tighter and tighter shapes. Victoria Rimell brings ideas and methods from literary theory, cultural studies and philosophy to bear on an extraordinary range of ancient texts rarely studied in juxtaposition, from Horace's Odes, Virgil's Aeneid and Ovid's Ibis, to Seneca's Letters, Statius' Achilleid and Tacitus' Annals. A series of epilogues puts these texts in conceptual dialogue with our own contemporary art world, and emphasizes the role Rome's imagination has played in the history of Western thinking about space, security and dwelling.

This book explores the notions of space and extension of major early modern empiricist philosophers, especially Locke, Berkeley, Hume, and Condillac. While space is a central and challenging issue for early modern empiricists, literature on this topic is sparse. This collection shows the diversity and problematic unity of empiricist views of space. Despite their common attention to the content of sensorial experience and to the analytical method, empiricist theories of space vary widely both in the way of approaching the issue and in the result of their investigation. However, by recasting the questions and examining the conceptual shifts, we see the emergence of a programmatic core, common to what the authors discuss. The introductory chapter describes this variety and its common core. The other contributions provide more specific perspectives on the issue of space within the philosophical literature. This book offers a unique overview of the early modern understanding of these issues, of interest to historians of early modern philosophy, historians and philosophers of science, historians of ideas, and all readers who want to expand their knowledge of the empiricist tradition.

Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.

Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).